TSTP Solution File: LCL498+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:38:02 EDT 2024
% Result : Theorem 74.54s 10.83s
% Output : CNFRefutation 74.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of formulae : 141 ( 45 unt; 0 def)
% Number of atoms : 279 ( 73 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 256 ( 118 ~; 112 |; 2 &)
% ( 13 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 236 ( 11 sgn 74 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f21,axiom,
( cn3
<=> ! [X3] : is_a_theorem(implies(implies(not(X3),X3),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
fof(f22,axiom,
( r1
<=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).
fof(f25,axiom,
( r4
<=> ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
fof(f26,axiom,
( r5
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r5) ).
fof(f45,conjecture,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f46,negated_conjecture,
~ cn3,
inference(negated_conjecture,[],[f45]) ).
fof(f52,plain,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(rectify,[],[f21]) ).
fof(f53,plain,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(rectify,[],[f22]) ).
fof(f54,plain,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(rectify,[],[f23]) ).
fof(f55,plain,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(rectify,[],[f24]) ).
fof(f56,plain,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(rectify,[],[f25]) ).
fof(f57,plain,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(rectify,[],[f26]) ).
fof(f58,plain,
~ cn3,
inference(flattening,[],[f46]) ).
fof(f59,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f60,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f61,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f62,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f63,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f64,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
=> cn3 ),
inference(unused_predicate_definition_removal,[],[f52]) ).
fof(f66,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f69,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f66]) ).
fof(f70,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
( cn3
| ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f73,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f63]) ).
fof(f74,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f62]) ).
fof(f75,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f61]) ).
fof(f76,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f60]) ).
fof(f77,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f59]) ).
fof(f80,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f82,plain,
( ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0))
=> ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f72,f82]) ).
fof(f84,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f70]) ).
fof(f86,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f87,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f88,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f89,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f75]) ).
fof(f90,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f76]) ).
fof(f91,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f77]) ).
fof(f94,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f80]) ).
fof(f96,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f99,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f100,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f101,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f102,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f103,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f104,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f108,plain,
~ cn3,
inference(cnf_transformation,[],[f58]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_51,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_52,plain,
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_53,plain,
( ~ r2
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_54,plain,
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_55,plain,
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_56,plain,
( ~ r5
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_59,plain,
( ~ op_implies_or
| or(not(X0),X1) = implies(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_61,plain,
op_implies_or,
inference(cnf_transformation,[],[f96]) ).
cnf(c_64,plain,
modus_ponens,
inference(cnf_transformation,[],[f99]) ).
cnf(c_65,plain,
r1,
inference(cnf_transformation,[],[f100]) ).
cnf(c_66,plain,
r2,
inference(cnf_transformation,[],[f101]) ).
cnf(c_67,plain,
r3,
inference(cnf_transformation,[],[f102]) ).
cnf(c_68,plain,
r4,
inference(cnf_transformation,[],[f103]) ).
cnf(c_69,plain,
r5,
inference(cnf_transformation,[],[f104]) ).
cnf(c_73,negated_conjecture,
~ cn3,
inference(cnf_transformation,[],[f108]) ).
cnf(c_84,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_66,c_53]) ).
cnf(c_87,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_65,c_52]) ).
cnf(c_92,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_67,c_54]) ).
cnf(c_95,plain,
or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_61,c_59]) ).
cnf(c_101,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_64,c_49]) ).
cnf(c_102,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_101]) ).
cnf(c_112,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(global_subsumption_just,[status(thm)],[c_56,c_69,c_56]) ).
cnf(c_115,plain,
is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_68,c_55]) ).
cnf(c_134,plain,
X0 = X0,
theory(equality) ).
cnf(c_136,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_137,plain,
( X0 != X1
| ~ is_a_theorem(X1)
| is_a_theorem(X0) ),
theory(equality) ).
cnf(c_138,plain,
( X0 != X1
| X2 != X3
| implies(X0,X2) = implies(X1,X3) ),
theory(equality) ).
cnf(c_139,plain,
( X0 != X1
| not(X0) = not(X1) ),
theory(equality) ).
cnf(c_143,plain,
( sK0 != sK0
| not(sK0) = not(sK0) ),
inference(instantiation,[status(thm)],[c_139]) ).
cnf(c_146,plain,
sK0 = sK0,
inference(instantiation,[status(thm)],[c_134]) ).
cnf(c_333,plain,
( or(X0,X1) != X2
| X3 != X2
| X3 = or(X0,X1) ),
inference(instantiation,[status(thm)],[c_136]) ).
cnf(c_447,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c_102,c_87]) ).
cnf(c_451,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[status(thm)],[c_102,c_92]) ).
cnf(c_506,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_137,c_95]) ).
cnf(c_550,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(or(X2,X0),or(X2,X1))) ),
inference(resolution,[status(thm)],[c_112,c_102]) ).
cnf(c_563,plain,
( ~ is_a_theorem(or(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(X0,X2))) ),
inference(resolution,[status(thm)],[c_115,c_102]) ).
cnf(c_600,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[status(thm)],[c_550,c_102]) ).
cnf(c_609,plain,
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(not(X0),X2))) ),
inference(resolution,[status(thm)],[c_563,c_506]) ).
cnf(c_662,plain,
( or(not(X0),X1) != implies(X0,X1)
| X2 != implies(X0,X1)
| X2 = or(not(X0),X1) ),
inference(instantiation,[status(thm)],[c_333]) ).
cnf(c_795,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_136,c_134]) ).
cnf(c_835,plain,
( X0 != X1
| X2 != X3
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[status(thm)],[c_138,c_137]) ).
cnf(c_994,plain,
implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c_795,c_95]) ).
cnf(c_1020,plain,
( ~ is_a_theorem(or(not(X0),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_994,c_137]) ).
cnf(c_1684,plain,
( X0 != X1
| X2 != or(X3,X1)
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[status(thm)],[c_835,c_84]) ).
cnf(c_2611,plain,
( or(not(X0),X1) != implies(X0,X1)
| implies(X2,X3) != implies(X0,X1)
| implies(X2,X3) = or(not(X0),X1) ),
inference(instantiation,[status(thm)],[c_662]) ).
cnf(c_4764,plain,
( X0 != X1
| is_a_theorem(implies(X0,or(X2,X1))) ),
inference(resolution,[status(thm)],[c_1684,c_134]) ).
cnf(c_4907,plain,
( X0 != X1
| ~ is_a_theorem(X0)
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[status(thm)],[c_4764,c_102]) ).
cnf(c_5330,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X2,or(not(X0),X1))) ),
inference(resolution,[status(thm)],[c_4907,c_994]) ).
cnf(c_6881,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(not(X0),or(X2,X1))) ),
inference(resolution,[status(thm)],[c_5330,c_563]) ).
cnf(c_8035,plain,
( X0 != or(X1,X2)
| X3 != X4
| implies(X0,X3) = implies(or(X1,X2),X4) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_8168,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,or(X2,X1))) ),
inference(resolution,[status(thm)],[c_6881,c_1020]) ).
cnf(c_8195,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[status(thm)],[c_8168,c_102]) ).
cnf(c_8397,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X2,or(X1,X0))) ),
inference(resolution,[status(thm)],[c_8195,c_92]) ).
cnf(c_9099,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,or(X2,X0))) ),
inference(resolution,[status(thm)],[c_8397,c_563]) ).
cnf(c_9248,plain,
( ~ is_a_theorem(or(X0,or(X1,X0)))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[status(thm)],[c_9099,c_447]) ).
cnf(c_16318,plain,
( X0 != implies(X1,X2)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X0) ),
inference(instantiation,[status(thm)],[c_137]) ).
cnf(c_18224,plain,
( implies(X0,X1) != or(not(X2),X3)
| X4 != X5
| implies(implies(X0,X1),X4) = implies(or(not(X2),X3),X5) ),
inference(instantiation,[status(thm)],[c_8035]) ).
cnf(c_20675,plain,
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_609,c_9248]) ).
cnf(c_21497,plain,
is_a_theorem(or(not(X0),X0)),
inference(resolution,[status(thm)],[c_20675,c_84]) ).
cnf(c_21539,plain,
is_a_theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[c_21497,c_451]) ).
cnf(c_21544,plain,
is_a_theorem(or(X0,or(not(or(X0,X1)),X1))),
inference(resolution,[status(thm)],[c_21497,c_563]) ).
cnf(c_21883,plain,
( ~ is_a_theorem(implies(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_21539,c_600]) ).
cnf(c_22759,plain,
is_a_theorem(implies(X0,or(not(or(not(X0),X1)),X1))),
inference(resolution,[status(thm)],[c_21544,c_1020]) ).
cnf(c_26125,plain,
( implies(X0,X1) != implies(X2,X3)
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(X0,X1)) ),
inference(instantiation,[status(thm)],[c_16318]) ).
cnf(c_32288,plain,
is_a_theorem(or(X0,or(not(or(not(not(X0)),X1)),X1))),
inference(resolution,[status(thm)],[c_22759,c_21883]) ).
cnf(c_40965,plain,
( implies(implies(not(sK0),sK0),sK0) != implies(X0,X1)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_26125]) ).
cnf(c_50930,plain,
( not(sK0) != X0
| sK0 != X1
| implies(not(sK0),sK0) = implies(X0,X1) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_50935,plain,
( or(not(X0),X1) != implies(X0,X1)
| implies(not(sK0),sK0) != implies(X0,X1)
| implies(not(sK0),sK0) = or(not(X0),X1) ),
inference(instantiation,[status(thm)],[c_2611]) ).
cnf(c_59057,plain,
is_a_theorem(or(not(or(not(not(X0)),X0)),X0)),
inference(resolution,[status(thm)],[c_32288,c_9248]) ).
cnf(c_59097,plain,
is_a_theorem(implies(or(not(not(X0)),X0),X0)),
inference(resolution,[status(thm)],[c_59057,c_1020]) ).
cnf(c_59100,plain,
is_a_theorem(implies(or(not(not(sK0)),sK0),sK0)),
inference(instantiation,[status(thm)],[c_59097]) ).
cnf(c_60752,plain,
( implies(not(sK0),sK0) != or(not(X0),X1)
| sK0 != X2
| implies(implies(not(sK0),sK0),sK0) = implies(or(not(X0),X1),X2) ),
inference(instantiation,[status(thm)],[c_18224]) ).
cnf(c_60754,plain,
( implies(implies(not(sK0),sK0),sK0) != implies(or(not(X0),X1),X2)
| ~ is_a_theorem(implies(or(not(X0),X1),X2))
| is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_40965]) ).
cnf(c_61583,plain,
( not(sK0) != not(X0)
| sK0 != X1
| implies(not(sK0),sK0) = implies(not(X0),X1) ),
inference(instantiation,[status(thm)],[c_50930]) ).
cnf(c_61585,plain,
( not(sK0) != not(sK0)
| sK0 != sK0
| implies(not(sK0),sK0) = implies(not(sK0),sK0) ),
inference(instantiation,[status(thm)],[c_61583]) ).
cnf(c_73538,plain,
( or(not(not(sK0)),sK0) != implies(not(sK0),sK0)
| implies(not(sK0),sK0) != implies(not(sK0),sK0)
| implies(not(sK0),sK0) = or(not(not(sK0)),sK0) ),
inference(instantiation,[status(thm)],[c_50935]) ).
cnf(c_73854,plain,
or(not(not(sK0)),sK0) = implies(not(sK0),sK0),
inference(instantiation,[status(thm)],[c_95]) ).
cnf(c_88463,plain,
( implies(not(sK0),sK0) != or(not(not(sK0)),sK0)
| sK0 != X0
| implies(implies(not(sK0),sK0),sK0) = implies(or(not(not(sK0)),sK0),X0) ),
inference(instantiation,[status(thm)],[c_60752]) ).
cnf(c_88464,plain,
( implies(not(sK0),sK0) != or(not(not(sK0)),sK0)
| sK0 != sK0
| implies(implies(not(sK0),sK0),sK0) = implies(or(not(not(sK0)),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_88463]) ).
cnf(c_101861,plain,
( implies(implies(not(sK0),sK0),sK0) != implies(or(not(not(sK0)),sK0),X0)
| ~ is_a_theorem(implies(or(not(not(sK0)),sK0),X0))
| is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_60754]) ).
cnf(c_101862,plain,
( implies(implies(not(sK0),sK0),sK0) != implies(or(not(not(sK0)),sK0),sK0)
| ~ is_a_theorem(implies(or(not(not(sK0)),sK0),sK0))
| is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_101861]) ).
cnf(c_101863,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_101862,c_88464,c_73854,c_73538,c_61585,c_59100,c_146,c_143,c_51,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 19:11:46 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 74.54/10.83 % SZS status Started for theBenchmark.p
% 74.54/10.83 % SZS status Theorem for theBenchmark.p
% 74.54/10.83
% 74.54/10.83 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 74.54/10.83
% 74.54/10.83 ------ iProver source info
% 74.54/10.83
% 74.54/10.83 git: date: 2024-05-02 19:28:25 +0000
% 74.54/10.83 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 74.54/10.83 git: non_committed_changes: false
% 74.54/10.83
% 74.54/10.83 ------ Parsing...
% 74.54/10.83 ------ Clausification by vclausify_rel & Parsing by iProver...
% 74.54/10.83
% 74.54/10.83 ------ Preprocessing... sf_s rm: 13 0s sf_e sf_s rm: 1 0s sf_e
% 74.54/10.83
% 74.54/10.83 ------ Preprocessing...
% 74.54/10.83
% 74.54/10.83 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 74.54/10.83 ------ Proving...
% 74.54/10.83 ------ Problem Properties
% 74.54/10.83
% 74.54/10.83
% 74.54/10.83 clauses 12
% 74.54/10.83 conjectures 0
% 74.54/10.83 EPR 0
% 74.54/10.83 Horn 12
% 74.54/10.83 unary 10
% 74.54/10.83 binary 1
% 74.54/10.83 lits 15
% 74.54/10.83 lits eq 5
% 74.54/10.83 fd_pure 0
% 74.54/10.83 fd_pseudo 0
% 74.54/10.83 fd_cond 0
% 74.54/10.83 fd_pseudo_cond 1
% 74.54/10.83 AC symbols 0
% 74.54/10.83
% 74.54/10.83 ------ Input Options Time Limit: Unbounded
% 74.54/10.83
% 74.54/10.83
% 74.54/10.83 ------
% 74.54/10.83 Current options:
% 74.54/10.83 ------
% 74.54/10.83
% 74.54/10.83
% 74.54/10.83
% 74.54/10.83
% 74.54/10.83 ------ Proving...
% 74.54/10.83
% 74.54/10.83
% 74.54/10.83 % SZS status Theorem for theBenchmark.p
% 74.54/10.83
% 74.54/10.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 74.54/10.83
% 74.54/10.83
%------------------------------------------------------------------------------